At this moment I am running a multilevel model with a cross-level interaction using the MLR estimator. Above my model results I find the following warning:

MAXIMUM LOG-LIKELIHOOD VALUE FOR THE UNRESTRICTED (H1) MODEL IS -1011.058

WARNING: THE MODEL ESTIMATION HAS REACHED A SADDLE POINT OR A POINT WHERE THE OBSERVED AND THE EXPECTED INFORMATION MATRICES DO NOT MATCH.AN ADJUSTMENT TO THE ESTIMATION OF THE INFORMATION MATRIX HAS BEEN MADE. THE CONDITION NUMBER IS -0.672D-03. THE PROBLEM MAY ALSO BE RESOLVED BY DECREASING THE VALUE OF THE MCONVERGENCE OR LOGCRITERION OPTIONS OR BY CHANGING THE STARTING VALUES OR BY USING THE MLF ESTIMATOR.

THE MODEL ESTIMATION TERMINATED NORMALLY

For me, this warning sounds like Mplus made an adjustment and that I can interpret my cross-level interaction. Is this correct? Or do I need to make an additional adjustment myself? The strange thing is that the cross-level interaction disappears when I change the estimator from MLR to MLF... Does this mean that the identified cross-level interaction is a statistical artefact?

I have also estimated a multilevel model to estimate a cross-level interaction and obtain a similar error message. I have two questions: (1) When is it safe to "ignore" the warning ? When it says that the model estimation terminated normally? And (2) how would you report this in an article? That an adjustment to the information matrix has been made and then make a reference to the article by Tihomir and Bengt on the issue http://www.statmodel.com/download/SaddlePoints2.pdf ? Or not mention it at all since the model estimated normally?

My warning message is this:

WARNING: THE MODEL ESTIMATION HAS REACHED A SADDLE POINT OR A POINT WHERE THE OBSERVED AND THE EXPECTED INFORMATION MATRICES DO NOT MATCH. AN ADJUSTMENT TO THE ESTIMATION OF THE INFORMATION MATRIX HAS BEEN MADE. THE CONDITION NUMBER IS -0.998D-03. THE PROBLEM MAY ALSO BE RESOLVED BY DECREASING THE VALUE OF THE MCONVERGENCE OR LOGCRITERION OPTIONS OR BY CHANGING THE STARTING VALUES OR BY USING THE MLF ESTIMATOR.

(1) I think it is typically safe to ignore the warning; it is mainly given as information about which SE estimator is used. If you can eliminate reasons 1. and 2. mentioned in the tech note that you refer to, then you should be fine.

(2) I would report that the SEs are computed with this method, giving a reference to the tech note.